Final answer:
The inverse of f(x) = 2x - 3 is f^-1(x) = (x + 3)/2, the inverse of f(x) = 4x + 10 is f^-1(x) = (x - 10)/4, and the inverse of f(x) = x^4 + 7 for x≥0 is g(x) = (x - 7)^1/4.
Step-by-step explanation:
The question asked pertains to finding the inverse of a function in various instances. An inverse function essentially reverses the action of the original function. For a function like f(x) = 2x - 3, the steps to find its inverse include swapping x and f(x), solving for the new f(x), which will be noted as f-1(x), the inverse function. Applying this to f(x) = 2x - 3 would yield x = 2y - 3, and solving for y gives us f-1(x) = (x + 3)/2.
Following a similar process for f(x) = 4x + 10, we switch x and y, giving x = 4y + 10, and solving for y leads to the inverse function f-1(x) = (x - 10)/4.
The inverse of f(x) = x4 + 7, considering x≥0, would be found by setting x = y4 + 7 and isolating y to determine g(x), which in this case involves taking the fourth root and subtracting 7 to find g(x) = (x - 7)1/4.